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For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [ 1 ] for an idealized simple pendulum is, approximately,
An example of a source of this uncertainty would be the drag in an experiment designed to measure the acceleration of gravity near the earth's surface. The commonly used gravitational acceleration of 9.8 m/s² ignores the effects of air resistance, but the air resistance for the object could be measured and incorporated into the experiment to ...
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
C-boxes (or confidence structures [16]) are estimators of fixed, real-valued quantities that depend on random sample data and encode Neyman [17] confidence intervals at every level of confidence. [ 18 ] [ 19 ] [ 16 ] They characterize the inferential uncertainty about the estimate in the form of a collection of focal intervals (or sets), each ...
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Uncertainty is traditionally modelled by a probability distribution, as developed by Kolmogorov, [1] Laplace, de Finetti, [2] Ramsey, Cox, Lindley, and many others.However, this has not been unanimously accepted by scientists, statisticians, and probabilists: it has been argued that some modification or broadening of probability theory is required, because one may not always be able to provide ...
[note 1] For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.
Quantitative uses of the terms uncertainty and risk are fairly consistent among fields such as probability theory, actuarial science, and information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes used in information theory ...